[Haskell-beginners] Enum for natural numbers

[Deniz Dogan]

2009/12/20  <kane96 at gmx.de>:
> Maybe I didn't understand the exercise if have to do. It says:
> "Write the instance Enum Nat where toEnum is defined as a total function that returns Z for negative integers. Some examples:
> *Main> toEnum (-1) :: Nat
> Z
> *Main> toEnum 0 :: Nat
> Z
> *Main> toEnum 1 :: Nat
> S Z
> *Main> fromEnum (S (S Z))
> 2
>
> so I did:
> data Nat = Z | S Nat deriving (Eq,Ord,Show)
> instance Enum Nat where
> toEnum x|x > 0 = S Z
>        |otherwise = Z
>
>
> somehow it looks really wrong. Do you understand want I have to do and how it should look like?
>

In your current definition of toEnum, you always return "S Z" (in
other words, "1", "the successor of zero") for any integer i > 0. This
is clearly incorrect as you said. Your "otherwise" guard is correct,
but the other one is not. I get the feeling that this exercise is
about learning how to use recursion, so look into that.

A few relevant links:
http://en.wikibooks.org/wiki/Haskell/Recursion (the factorial example)
http://learnyouahaskell.com/recursion
http://book.realworldhaskell.org/read/functional-programming.html

Hope that helps

-- 
Deniz Dogan